# Download A TREATISE ON THE MATHEMATICAL THEORY OF ELASTICITY by A. E. H. LOVE PDF

By A. E. H. LOVE

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Example text

Join Can-i to An, this determines the last side of the funicular. From the point where it meets the line of action of F^, draw a line and produce this to meet the vertical through a^-/ ^^ Join Vn-i to G3n-4 and proceed in the same way, and we obtain the funicular. The side (Sn — S) of the funicular will be to G^n-iy Vn-i' found by joining the points where (^n — 2) meets the vertical — through gn and where (3n 4) meets the vertical through g'n-i. This side must pass through An-i. The sides may be constructed in like manner.

BENDING OF RODS IN ONE PLANE. 48 If therefore makes with the the rod we have /ds, and the third gives us jg^ + i2sin<^ = (61). This equation can be identified with the equation of motion moving about a fixed horizontal axis as of a heavy rigid body follows : B the moment of inertia of the rigid represent the time, the weight of the body, and let body about the fixed axis, and the centre of inertia of the body be at unit distance from the fixed Let s R axis, the above equation (61) is the equation of motion of the of inertia and the fixed body when the plane through the centre axis makes an angle with the vertical.

The side (Sn — S) of the funicular will be to G^n-iy Vn-i' found by joining the points where (^n — 2) meets the vertical — through gn and where (3n 4) meets the vertical through g'n-i. This side must pass through An-i. The sides may be constructed in like manner. (3/1 — 6), (3n — 9)... The bending moments at the supports may also be found Let the vertical through Ar meet the side (3r + 1) graphically. in Sr, then Ar Sr/Ar A\+i is proportional to the bending moment We have seen that if Ar A'r be drawn to represent the at Ar.